Least Common Multiple of 2198 and 2200

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2198 and 2200 the smallest integer that is 2417800 that is divisible by both numbers.

Least Common Multiple (LCM) of 2198 and 2200 is 2417800.

LCM(2198,2200) = 2417800

LCM of 2198 and 2200

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 2198 and 2200

LCM of 2198 and 2200 is 2417800

Least common multiple can be found by multiplying the highest exponent prime factors of 2198 and 2200. First we will calculate the prime factors of 2198 and 2200.

Prime Factorization of 2198


2 2198
7 1099
157 157
1

Prime factors of 2198 are 2, 7,157. Prime factorization of 2198 in exponential form is:

2198 = 21×71×1571

Prime Factorization of 2200


2 2200
2 1100
2 550
5 275
5 55
11 11
1

Prime factors of 2200 are 2, 5,11. Prime factorization of 2200 in exponential form is:

2200 = 23×52×111

Now multiplying the highest exponent prime factors to calculate the LCM of 2198 and 2200.

LCM(2198,2200) = 23×52×71×111×1571
LCM(2198,2200) = 2417800

Factors of 2198

List of positive integer factors of 2198 that divides 2198 without a remainder.

1, 2, 7, 14, 157, 314, 1099, 2198

Factors of 2200

List of positive integer factors of 2200 that divides 2200 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200

Least Common Multiple of 2198 and 2200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2198 and 2200, than apply into the LCM equation.

GCF(2198,2200) = 2
LCM(2198,2200) = ( 2198 × 2200) / 2
LCM(2198,2200) = 4835600 / 2
LCM(2198,2200) = 2417800

Properties of LCM 2198 and 2200

(i) The LCM of 2200 and 2198 is associative

LCM of 2198 and 2200 = LCM of 2200 and 2198

Related Least Common Multiples of 2198

Related Least Common Multiples of 2200

Frequently Asked Questions on LCM of 2198 and 2200

1. What is the LCM of 2198 and 2200?

Answer: LCM of 2198 and 2200 is 2417800.

2. What are the Factors of 2198?

Answer: Factors of 2198 are 1, 2, 7, 14, 157, 314, 1099, 2198. There are 8 integers that are factors of 2198. The greatest factor of 2198 is 2198.

3. What are the Factors of 2200?

Answer: Factors of 2200 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200. There are 24 integers that are factors of 2200. The greatest factor of 2200 is 2200.

4. How to Find the LCM of 2198 and 2200?

Answer:

Least Common Multiple of 2198 and 2200 = 2417800

Step 1: Find the prime factorization of 2198

2198 = 2 x 7 x 157

Step 2: Find the prime factorization of 2200

2200 = 2 x 2 x 2 x 5 x 5 x 11

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2417800 = 2 x 2 x 2 x 5 x 5 x 7 x 11 x 157

Step 4: Therefore, the least common multiple of 2198 and 2200 is 2417800.